1. **Problem Statement:** Graph the function $s(d)$ where $s$ is the speed in miles per hour and $d$ is the distance in feet the driver brakes. 2. **Understanding the problem:** We are given points approximately at $(10,30)$ and $(25,35)$ on the graph where the first coordinate is $d$ (distance) and the second is $s$ (speed). 3. **Plotting points:** - Leftmost point: $(10,30)$ - Three additional points: We only have one more given point $(25,35)$, so we need to estimate or find two more points to complete the four points. 4. **Assuming a linear relationship for simplicity:** The speed increases as the braking distance increases. 5. **Finding the equation of the line through points $(10,30)$ and $(25,35)$:** Slope $m = \frac{35-30}{25-10} = \frac{5}{15} = \frac{1}{3}$ 6. **Equation of the line:** Using point-slope form: $$s - 30 = \frac{1}{3}(d - 10)$$ Simplify: $$s = \frac{1}{3}d - \frac{10}{3} + 30 = \frac{1}{3}d + \frac{80}{3}$$ 7. **Calculate two more points using this equation:** - For $d=15$: $$s = \frac{1}{3} \times 15 + \frac{80}{3} = 5 + \frac{80}{3} = \frac{15}{3} + \frac{80}{3} = \frac{95}{3} \approx 31.67$$ - For $d=20$: $$s = \frac{1}{3} \times 20 + \frac{80}{3} = \frac{20}{3} + \frac{80}{3} = \frac{100}{3} \approx 33.33$$ 8. **Summary of points to graph:** - $(10,30)$ - $(15,31.67)$ - $(20,33.33)$ - $(25,35)$ These points can be plotted to graph the function $s(d)$. **Final answer:** $$s(d) = \frac{1}{3}d + \frac{80}{3}$$